The direct-flow Coriolis mass flowmeter comprises a tensioned section of string, along which a substance to be measured flows, a device for tensioning the section of string, a device for exciting a transverse circular oscillatory movement in the string, two sensors which are spaced apart along the string and which convert the magnitude of a transverse deflection of the string in two mutually perpendicular directions into electrical signals, wherein these signals are coupled to inputs of a microprocessor device which calculates the flowrate as a function of the difference in phases of the signals from the sensors.